313 lines
8.1 KiB
Fortran
313 lines
8.1 KiB
Fortran
*> \brief \b SQRT15
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
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* RANK, NORMA, NORMB, ISEED, WORK, LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
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* REAL NORMA, NORMB
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SQRT15 generates a matrix with full or deficient rank and of various
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*> norms.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] SCALE
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*> \verbatim
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*> SCALE is INTEGER
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*> SCALE = 1: normally scaled matrix
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*> SCALE = 2: matrix scaled up
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*> SCALE = 3: matrix scaled down
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*> \endverbatim
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*>
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*> \param[in] RKSEL
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*> \verbatim
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*> RKSEL is INTEGER
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*> RKSEL = 1: full rank matrix
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*> RKSEL = 2: rank-deficient matrix
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of A.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of B.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The M-by-N matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A.
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is REAL array, dimension (LDB, NRHS)
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*> A matrix that is in the range space of matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B.
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is REAL array, dimension MIN(M,N)
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*> Singular values of A.
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*> \endverbatim
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*>
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*> \param[out] RANK
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*> \verbatim
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*> RANK is INTEGER
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*> number of nonzero singular values of A.
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*> \endverbatim
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*>
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*> \param[out] NORMA
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*> \verbatim
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*> NORMA is REAL
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*> one-norm of A.
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*> \endverbatim
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*>
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*> \param[out] NORMB
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*> \verbatim
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*> NORMB is REAL
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*> one-norm of B.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is integer array, dimension (4)
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*> seed for random number generator.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> length of work space required.
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*> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
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$ RANK, NORMA, NORMB, ISEED, WORK, LWORK )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
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REAL NORMA, NORMB
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE, TWO, SVMIN
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
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$ SVMIN = 0.1E0 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO, J, MN
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REAL BIGNUM, EPS, SMLNUM, TEMP
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* ..
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* .. Local Arrays ..
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REAL DUMMY( 1 )
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* ..
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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANGE, SLARND, SNRM2
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EXTERNAL SASUM, SLAMCH, SLANGE, SLARND, SNRM2
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SLAORD, SLARF, SLARNV, SLAROR, SLASCL,
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$ SLASET, SSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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MN = MIN( M, N )
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IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN
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CALL XERBLA( 'SQRT15', 16 )
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RETURN
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END IF
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*
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SMLNUM = SLAMCH( 'Safe minimum' )
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BIGNUM = ONE / SMLNUM
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EPS = SLAMCH( 'Epsilon' )
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SMLNUM = ( SMLNUM / EPS ) / EPS
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BIGNUM = ONE / SMLNUM
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*
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* Determine rank and (unscaled) singular values
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*
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IF( RKSEL.EQ.1 ) THEN
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RANK = MN
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ELSE IF( RKSEL.EQ.2 ) THEN
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RANK = ( 3*MN ) / 4
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DO 10 J = RANK + 1, MN
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S( J ) = ZERO
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10 CONTINUE
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ELSE
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CALL XERBLA( 'SQRT15', 2 )
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END IF
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*
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IF( RANK.GT.0 ) THEN
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*
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* Nontrivial case
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*
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S( 1 ) = ONE
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DO 30 J = 2, RANK
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20 CONTINUE
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TEMP = SLARND( 1, ISEED )
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IF( TEMP.GT.SVMIN ) THEN
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S( J ) = ABS( TEMP )
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ELSE
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GO TO 20
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END IF
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30 CONTINUE
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CALL SLAORD( 'Decreasing', RANK, S, 1 )
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*
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* Generate 'rank' columns of a random orthogonal matrix in A
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*
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CALL SLARNV( 2, ISEED, M, WORK )
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CALL SSCAL( M, ONE / SNRM2( M, WORK, 1 ), WORK, 1 )
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CALL SLASET( 'Full', M, RANK, ZERO, ONE, A, LDA )
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CALL SLARF( 'Left', M, RANK, WORK, 1, TWO, A, LDA,
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$ WORK( M+1 ) )
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*
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* workspace used: m+mn
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*
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* Generate consistent rhs in the range space of A
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*
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CALL SLARNV( 2, ISEED, RANK*NRHS, WORK )
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CALL SGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, ONE,
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$ A, LDA, WORK, RANK, ZERO, B, LDB )
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*
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* work space used: <= mn *nrhs
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*
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* generate (unscaled) matrix A
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*
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DO 40 J = 1, RANK
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CALL SSCAL( M, S( J ), A( 1, J ), 1 )
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40 CONTINUE
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IF( RANK.LT.N )
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$ CALL SLASET( 'Full', M, N-RANK, ZERO, ZERO, A( 1, RANK+1 ),
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$ LDA )
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CALL SLAROR( 'Right', 'No initialization', M, N, A, LDA, ISEED,
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$ WORK, INFO )
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*
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ELSE
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*
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* work space used 2*n+m
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*
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* Generate null matrix and rhs
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*
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DO 50 J = 1, MN
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S( J ) = ZERO
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50 CONTINUE
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CALL SLASET( 'Full', M, N, ZERO, ZERO, A, LDA )
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CALL SLASET( 'Full', M, NRHS, ZERO, ZERO, B, LDB )
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*
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END IF
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*
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* Scale the matrix
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*
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IF( SCALE.NE.1 ) THEN
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NORMA = SLANGE( 'Max', M, N, A, LDA, DUMMY )
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IF( NORMA.NE.ZERO ) THEN
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IF( SCALE.EQ.2 ) THEN
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*
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* matrix scaled up
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*
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CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A,
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$ LDA, INFO )
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CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S,
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$ MN, INFO )
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CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B,
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$ LDB, INFO )
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ELSE IF( SCALE.EQ.3 ) THEN
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*
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* matrix scaled down
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*
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CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A,
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$ LDA, INFO )
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CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S,
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$ MN, INFO )
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CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B,
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$ LDB, INFO )
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ELSE
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CALL XERBLA( 'SQRT15', 1 )
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RETURN
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END IF
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END IF
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END IF
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*
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NORMA = SASUM( MN, S, 1 )
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NORMB = SLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY )
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*
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RETURN
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*
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* End of SQRT15
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*
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END
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